Suchergebnisse

Modelling and forecasting high dimensional covariance matrices is a key challenge in data-richenvironments involving even thousands of time series since most of the available models sufferfrom the curse of dimensionality. In this paper, we challenge some popular multivariate GARCH(MGARCH) and Stochastic Volatility (MSV) models by fitting them to forecast the conditionalcovariance matrices of financial portfolios with dimension up to 1000 assets observed daily over a30-year time span. The time evolution of the conditional variances and covariances estimated bythe different models is compared and evaluated in the context of a portfolio selection exercise. Weconclude that, in a realistic context in which transaction costs are taken into account, modelling thecovariance matrices as latent Wishart processes delivers more stable optimal portfolio compositionsand, consequently, higher Sharpe ratios. ; Guilherme V. Moura is supported by the Brazilian Government through grants number 424942- 2016-0 (CNPQ) and 302865-2016-0 (CNPQ). André A.P. Santos is supported by the Brazilian Government through grants number 303688-2016-5 (CNPQ) and 420038-2018-3 (CNPQ). Esther Ruiz is supported by the Spanish Government through grant number ECO2015-70331-C2-2-R (MINECO/FEDER).

We propose a novel approach to active risk management based on the recent Basel II regulations to obtain optimal portfolios with minimum capital requirements. In order to avoid regulatory penalties due to an excessive number of Value-at-Risk (VaR) violations, capital requirements are minimized subject to a given number of violations over the previous trading year. Capital requirements are based on the recent Basel II amendments to account for the 'stressed' VaR, that is, the downside risk of the portfolio under extreme adverse market conditions. An empirical application for two portfolios involving different types of assets and alternative stress scenarios demonstrates that the proposed approach delivers an improved balance between capital requirement levels and the number of VaR exceedances. Furthermore, the riskadjusted performance of the proposed approach is superior to that of minimum-VaR and minimumstressed VaR portfolios. ; André A. P. Santos acknowledges financial support from research Projects CNPq 481719/2011 3 and UFSC Funpesquisa 2010/2011 from the Brazilian Government. Francisco J. Nogales is supported by the Spanish Government through Project MTM 2010 16519. Esther Ruiz is supported by the Spanish Government ECO2009 08100 ; Publicado